Abstract
Human proximity networks are temporal networks representing the close-range proximity among humans in a physical space. They have been extensively studied in the past 15 years as they are critical for understanding the spreading of diseases and information among humans. Here we address the problem of mapping human proximity networks into hyperbolic spaces. Each snapshot of these networks is often very sparse, consisting of a small number of interacting (i.e., non-zero degree) nodes. Yet, we show that the time-aggregated representation of such systems over sufficiently large periods can be meaningfully embedded into the hyperbolic space, using methods developed for traditional (non-mobile) complex networks. We justify this compatibility theoretically and validate it experimentally. We produce hyperbolic maps of six different real systems, and show that the maps can be used to identify communities, facilitate efficient greedy routing on the temporal network, and predict future links with significant precision. Further, we show that epidemic arrival times are positively correlated with the hyperbolic distance from the infection sources in the maps. Thus, hyperbolic embedding could also provide a new perspective for understanding and predicting the behavior of epidemic spreading in human proximity systems.
Highlights
Human proximity networks are temporal networks representing the close-range proximity among humans in a physical space
We consider the following face-to-face interaction networks from SocioPatterns14. (i) A hospital ward in Lyon[11], which corresponds to interactions involving patients and healthcare workers during five observation days. (ii) A primary school in Lyon[10], which corresponds to interactions involving children and teachers of ten different classes during two days. (iii) A scientific conference in Turin[9], which corresponds to interactions among conference attendees during two and a half days. (iv) A high school in M arseilles[12], which corresponds to interactions among students of nine different classes during five days
Each snapshot corresponds to an observation interval of 5 min, while proximity was recorded if participants were within a radius of 10 m from each other
Summary
Human proximity networks are temporal networks representing the close-range proximity among humans in a physical space. Understanding the time-varying proximity patterns among humans in a physical space is crucial for better understanding the transmission of airborne diseases, the efficiency of information dissemination, social behavior, and influence[1,2,3,4,5,6,7,8] To this end, human proximity networks have been captured in different environments over days, weeks or months[2,4,5,9,10,11,12,13]. The probability that two nodes are connected in a snapshot generated by the model resembles the connection probability in the popular S1 model of traditional (non-mobile) complex networks, which is equivalent to random hyperbolic g raphs[20,21,22] Based on this observation, the dynamic-S1 model has been recently suggested as a minimal latent-space model for human proximity networks[22].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
